Esmerelda rents a car from a company that rents cars by the hour. She has to pay an initial fee of $52, and then they charge her $8 per hour. She has $144 available to spend on car rental. What is the greatest number of hours for which she can rent the car? (The car cannot be rented for part of an hour.)
Let x be the number of hours Esmerelda can rent the car for.
The total cost of renting the car will be:
$52 + $8x
Since she has $144 available to spend, we can write the equation:
$52 + $8x = $144
Subtracting $52 from both sides:
$8x = $92
Dividing both sides by $8:
x = 11.5
Since the car cannot be rented for part of an hour, the greatest number of hours for which she can rent the car is 11 hours.